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Peer-reviewedCC BYProceedings of the London Mathematical Society

Manin's conjecture for integral points on toric varieties

  • Tim Santens1
  1. 1University of Cambridge, DPMMS Centre for Mathematical Sciences Cambridge UK
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Abstract

We formulate a conjecture on the number of integral points of bounded height on log Fano varieties in analogy with Manin's conjecture on the number of rational points of bounded height on Fano varieties. We also give a prediction for the leading constant that is similar to Peyre's interpretation of the leading constant in Manin's conjecture. We give evidence for our conjecture by proving it for toric varieties. The proof is based on harmonic analysis on universal torsors.

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Cite

BibTeXRIS
BibTeX
@article{santens2026manins,
  title = {{Manin's conjecture for integral points on toric varieties}},
  author = {Tim Santens},
  journal = {Proceedings of the London Mathematical Society},
  year = {2026},
  month = aug,
  doi = {10.1112/plms.70203},
  url = {https://doi.org/10.1112/plms.70203},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Manin's conjecture for integral points on toric varieties
AU  - Tim Santens
PY  - 2026
DA  - 2026/08/01
JO  - Proceedings of the London Mathematical Society
DO  - 10.1112/plms.70203
UR  - https://doi.org/10.1112/plms.70203
AB  - We formulate a conjecture on the number of integral points of bounded height on log Fano varieties in analogy with Manin's conjecture on the number of rational points of bounded height on Fano varieties. We also give a prediction for the leading constant that is similar to Peyre's interpretation of the leading constant in Manin's conjecture. We give evidence for our conjecture by proving it for toric varieties. The proof is based on harmonic analysis on universal torsors.
SN  - 0024-6115
SN  - 1460-244X
ER  -